Generally in electromagnetic transient simulations, there are two basic methods to represent transmission systems. The first is the -section approach, where multi–phase systems can be characterized by a circuit of lumped passive elements. The second and more acknowledged method is a distributed parameter representation. Unlike the lumped element -section, a distributed model operates on the principle of traveling waves. A voltage disturbance will travel along a conductor at its propagation velocity (near the speed of light), until it is reflected at the other end. In an ideal sense, a distributed transmission system is a delay function; whatever is fed into one end will appear at the other end, perhaps slightly distorted, following some delay.
Both p-sections and distributed systems can be modeled with EMTDC. Distributed models are further sub-divided into single-frequency, and frequency-dependent representations. The constants required by EMTDC to represent distributed systems are calculated by a separate program called the Line Constants Program or LCP (discussed in the next section), whereas p-section representations are executed entirely within EMTDC.
Figure 8-1 –Transmission System Modeling Techniques in EMTDC
A p-section model will give the correct fundamental impedance, but cannot accurately represent other frequencies unless many sections are used (which is inefficient). It is suitable for very short lines where the travelling wave models cannot be used, due to time step constraints. In EMTDC, p-sections are not considered a very elegant means of transmission line modeling for the following reasons:
Greater computational time and increased EMTDC conductance matrix sizes
Do not represent propagation delay
Not practical with a large number of mutually coupled conductors
Frequency dependent attenuation of the traveling waves is not easily or accurately incorporated
P-sections are discussed in detail later in this chapter.
The Bergeron model is the simplest, oldest and least accurate of the distributed branch models in PSCAD – mainly due to the fact that it is not frequency-dependent (calculates at a single frequency).
The Bergeron model represents the system L and C in a distributed manner (as opposed to lumped elements as in p-sections). In fact, it is roughly equivalent to using an infinite number of series-connected p-sections except that the total system resistance R is lumped (½ in the middle of the line, ¼ at each end). As with p-sections, the Bergeron model accurately represents system parameters at the fundamental frequency. However, it can also be used to approximate higher frequency attenuation by choosing an additional frequency for calculation.
The Bergeron model is suitable for studies where frequencies other than the fundamental are of little or no concern (i.e. many load flow and protection studies). Situations where this model should be chosen over the more accurate frequency dependent models include; when a lack of frequency dependent input data exists (such as when only +, -, and 0 sequence data is known), and/or when computational speed over accuracy is more important.
The Bergeron model is discussed in more detail later in this chapter.
The frequency dependent models strive to represent the full frequency dependence of a transmission system. This is accomplished by solving the line parameters at many frequency points within a user-defined scope. As such, the frequency dependent models will take longer to solve than the Bergeron model, but are necessary for studies requiring a very detailed representation of the system over a wide frequency range. Unlike the Bergeron model, these models also represent the total system resistance R as a distributed parameter (along with a distributed system L and C), providing a much more accurate representation of attenuation.
PSCAD offers two frequency dependent models:
For all new studies involving transmission lines or cables, it is recommended that the Frequency Dependent (Phase) model be used. This model is the newest of the two (c. 1998) and was added to PSCAD specifically to replace the Frequency Dependent (Mode) model, which has been carried over from PSCAD V2 to allow for compatibility with older projects. The Frequency Dependent (Phase) model can represent any type of transmission system (i.e. aerial and underground, symmetrical and non-symmetrical) and is more accurate and more stable than its predecessor. The Frequency Dependent (Phase) model should normally be the model of choice for most studies.
The frequency dependent line models are discussed in more detail later in this chapter.